Rewrite as a simplified fraction. ${0.3\overline{21} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 321.2121...\\ 10x &= 3.2121...\end{align*}}$ Subtracting the two equations, we have: ${990x = 318}$ ${x = \dfrac{318}{990}} $ ${x = \dfrac{53}{165}} $